A butyl rubber has an extremely low degree of unsaturation and therefore, is superior in weather resistance, heat resistance, ozone resistance, etc. and has a low air permeability. Accordingly, the butyl rubber is being used as sealants, binders, etc. As the method of cross-linking a butyl rubber, sulfur cross-linking, quinoid cross-linking, resin cross-linking, etc. are known, but it is hard to say that practically satisfactory results are obtained by any method at present. That is, the sulfur cross-linking requires cross-linking at a high temperature over a long time. Further the quinoid cross-linking usually uses harmful red lead as an oxidant for activating the quinoid, and therefore, has environmental problems. Further, the resin cross-linking is remarkably slow in reaction rate and requires heating at a high temperature for a long time. The product is liable to be formed in a state not completely cross-linked, and therefore, there are the problems that, during use, the cross-linking reaction is liable to proceed and the physical properties are liable to be greatly changed. Further, among these cross-linking methods of diene-based rubber, etc., cross-linking by an organic peroxide extremely superior in the heat resistance is not being used much at all as a method of cross-linking butyl rubber. This is because, if this cross-linking is applied to a butyl rubber, the decomposition reaction of the main chain is liable to predominantly occur and the rubber is liable to be conversely softened, rather than the cross-linking. On the other hand, partially cross-linked butyl rubber is commercially available as a butyl rubber for which peroxide cross-linking is possible, but this has the problem that the processability is not sufficient. Further, Patent Document 1 discloses the method for cross-linking un-cross-linked butyl rubber in the presence of an organic peroxide and a polyfunctional monomer having electron acceptor groups, but according to this method, severe reversion is liable to occur.
Under these circumstances, the inventors previously proposed a modified rubber composition superior in weather resistance, heat resistance, ozone resistance, etc. and enabling an ordinary butyl rubber having a low air barrier property to be cross-linked with an organic peroxide (see Patent Document 2).    Patent Document 1: Japanese Patent Publication (A) No. 6-172547    Patent Document 2: Japanese Patent Application No. 2006-131780